"That means that a difference between two candidates that is less than twice the margin of error is considered statistically insignificant."

Shouldn't it be 1.414 times the margin of error instead of "twice"? The SD of the difference between two means is the square root of the sum of the SDs. So the multiplier should be the square root of 2, not 2 itself.

3:22 pm December 7, 2007

JCN wrote:

Phil is correct, but that is if you want to treat a 1 SD diff as "statistically significant" which most people would not do. 2.8 SD (2 * 1.4) would be more like it.

But that also assumes that the % voting for each candidate is independent, which it is not.

This had bothered me for years. If there are 2 candidates that are 55% to 45% in the polls, one is said to be "10% ahead" of the other."

But if only 5% of the voters change their minds, the candidates are tied ...

4:11 pm December 10, 2007

Phil Birnbaum wrote:

Good points by JCN ... 2.8 SD would be correct for that example. And he's right that if there are only two candidates, then you take the difference between the candidates and 50%, not the difference between them. So 2 SD would be correct there.

Good catch.

9:48 pm December 10, 2007

J.J. wrote:

Hey y'all, I believe that the article is written correctly and your suggestions are wrong. If I remember correctly, the "margin of error" for the entire poll is typically just another phrase meaning the "95% confidence interval given an observed proportion p of 0.5". In other words, it is already reported as an upper bound of the the 95% confidence interval, and thus needs no translation FROM a standard deviation to a C.I., because it is already a C.I. Note that this C.I. is quoted for the proportion with the maximum variance, at p = 0.5. For a less conservative estimate of the 95% C.I. for a poll, the equation is:

sqrt(pq/n),

where p is the proportion of interest, q = 1 - p, and n is the number of people surveyed.

2:08 pm December 11, 2007

Roger Green wrote:

I guess that I prefer erring on the side of "statistical tie" than when the news folks indicate that candidate X is beating Y but losing to candidate Z, each by less than the margin of error, which I've seen way too often.

11:36 am December 29, 2007

Inquirer wrote:

The whole thing about statisitcal tie is nonsense.

If Candidate A leads Candidate B 29 to 27, then Candidate A leads Candidate B 29 to 27.

The media, which relishes a horse race, blows margin of error and statistical tie way, way out of proportion in order to fabricate a "tie." It's about news, not about the accuracy of the poll.

More to the point is the wording of the questions in a poll. Thus it is well to look at a number of polls rather than just one. But beware: A poll that seems an anomaly can, in fact, be correct. In such a case, look at the record in recent times of the outfit making the poll.

My advice: Remember, that oftimes a cigar is just a cigar. If your candidate is ahead, your candidate indeed is ahead.

If you have a difficult time believing this, then research for yourselves the Presidential polling of the last several years. The polls were right on the mark despite the closeness of the race. The polls showed Al Gore the winner in 2000 and indeed he defeated Bush in the popular vote. The polls showed Bush narrowly defeating Kerry and you know that outcome.

The very real concern in political polling in the coming Presidential race is the opportunity for fraud at the polling places brought about by tampering by election officials with voting machines. The polls will be dead on; but the results might differ due to out and out fraud.

5:04 pm January 3, 2008

Bob wrote:

I agree with Roger Green. It has taken decades of work within journalism to get even some reporters to use the margin of error in interpreting poll results...and to do so in such a way that the average member of the public can make some sense of it (using the admittedly inaccurate phrase "statistical tie" does that). Too often, even to this day, reporters do what Roger Green observed...and I sense the trend is getting worse.

2:10 am January 5, 2008

Joe wrote:

The most egregious misuse of "statistical tie" in news reports about yesterday's Iowa caucus vote was the characterization last night on one network of the results for McCain and Thompson as being a statistical tie for 3rd place. There was no "tie" at all, as far as we can tell. Thompson has a slight lead, but not all precincts had reported by this morning. There's nothing "statistical" at all about an actual vote count.

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The Wall Street Journal examines numbers in the news, business and politics. Some numbers are flat-out wrong or biased, while others are valid and help us make informed decisions. We tell the stories behind the stats in occasional updates on this blog.